A Stability Technique for Evolution Partial Differential Equations: A Dynamical Systems Approach: 56 (Progress in Nonlinear Differential Equations and Their Applications) - Tapa dura

Galaktionov, Victor A.; Vázquez, Juan Luis

 
9780817641467: A Stability Technique for Evolution Partial Differential Equations: A Dynamical Systems Approach: 56 (Progress in Nonlinear Differential Equations and Their Applications)
Tapa dura
ISBN 10: 0817641467 ISBN 13: 9780817641467
Editorial: Birkhäuser, 2003

Sinopsis

common feature is that these evolution problems can be formulated as asymptoti­ cally small perturbations of certain dynamical systems with better-known behaviour. Now, it usually happens that the perturbation is small in a very weak sense, hence the difficulty (or impossibility) of applying more classical techniques. Though the method originated with the analysis of critical behaviour for evolu­ tion PDEs, in its abstract formulation it deals with a nonautonomous abstract differ­ ential equation (NDE) (1) Ut = A(u) + C(u, t), t > 0, where u has values in a Banach space, like an LP space, A is an autonomous (time-independent) operator and C is an asymptotically small perturbation, so that C(u(t), t) ~ ° as t ~ 00 along orbits {u(t)} of the evolution in a sense to be made precise, which in practice can be quite weak. We work in a situation in which the autonomous (limit) differential equation (ADE) Ut = A(u) (2) has a well-known asymptotic behaviour, and we want to prove that for large times the orbits of the original evolution problem converge to a certain class of limits of the autonomous equation. More precisely, we want to prove that the orbits of (NDE) are attracted by a certain limit set [2* of (ADE), which may consist of equilibria of the autonomous equation, or it can be a more complicated object.

"Sinopsis" puede pertenecer a otra edición de este libro.

Críticas

"The authors are famous experts in the field of PDEs and blow-up techniques. In this book they present a stability theorem, the so-called S-theorem, and show, with several examples, how it may be applied to a wide range of stability problems for evolution equations. The book [is] aimed primarily aimed at advanced graduate students."

―Mathematical Reviews

"The book is very interesting and useful for researchers and students in mathematical physics...with basic knowledge in partial differential equations and functional analysis. A comprehensive index and bibliography are given" ---Revue Roumaine de Mathématiques Pures et Appliquées

Reseña del editor

* Introduces a state-of-the-art method for the study of the asymptotic behavior of solutions to evolution partial differential equations.

* Written by established mathematicians at the forefront of their field, this blend of delicate analysis and broad application is ideal for a course or seminar in asymptotic analysis and nonlinear PDEs.

* Well-organized text with detailed index and bibliography, suitable as a course text or reference volume.

"Sobre este título" puede pertenecer a otra edición de este libro.

Editorial
Birkhäuser
Año de publicación
2003
Idioma
Inglés
ISBN 10 
0817641467
ISBN 13 
9780817641467
Encuadernación
Tapa dura
Número de páginas
400
Contacto del fabricante
no disponible
Persona responsable
no disponible

Otras ediciones populares con el mismo título

9781461273967: A Stability Technique for Evolution Partial Differential Equations: A Dynamical Systems Approach: 56 (Progress in Nonlinear Differential Equations and Their Applications)

Edición Destacada

ISBN 10:  146127396X ISBN 13:  9781461273967
Editorial: Birkhäuser, 2012
Tapa blanda